Solving Singularly Perturbed Differential Difference Equations via Fitted Method

Authors

Awoke Andargie, Bahir Dar University
Y. N. Reddy, National Institute of Technology

Abstract

In this paper, we presented a fitted approach to solve singularly perturbed differential difference equations of second order with boundary at one end (left or right) of the interval. In this approach, with the help of Taylor series expansion, we approximated the terms containing negative and positive shifts and modified the singularly perturbed differential difference equation to singularly perturbed differential equation. A fitting parameter in the coefficient of the highest order derivative of the new equation is introduced and determined its value from the theory of singular perturbation. Finally, we obtained a three term recurrence relation which is solved using Thomas Algorithm. The applicability of the method is tested with six linear problems.

Recommended Citation

Andargie, Awoke and Reddy, Y. N. (2013). Solving Singularly Perturbed Differential Difference Equations via Fitted Method, Applications and Applied Mathematics: An International Journal (AAM), Vol. 8, Iss. 1, Article 19.
Available at: https://digitalcommons.pvamu.edu/aam/vol8/iss1/19